Minimization of metabolic cost of transport predicts changes in gait mechanics over a range of ankle-foot orthosis stiffnesses in individuals with bilateral plantar flexor weakness

Neuromuscular disorders often lead to ankle plantar flexor muscle weakness, which impairs ankle push-off power and forward propulsion during gait. To improve walking speed and reduce metabolic cost of transport (mCoT), patients with plantar flexor weakness are provided dorsal-leaf spring ankle-foot orthoses (AFOs). It is widely believed that mCoT during gait depends on the AFO stiffness and an optimal AFO stiffness that minimizes mCoT exists. The biomechanics behind why and how an optimal stiffness exists and benefits individuals with plantar flexor weakness are not well understood. We hypothesized that the AFO would reduce the required support moment and, hence, metabolic cost contributions of the ankle plantar flexor and knee extensor muscles during stance, and reduce hip flexor metabolic cost to initiate swing. To test these hypotheses, we generated neuromusculoskeletal simulations to represent gait of an individual with bilateral plantar flexor weakness wearing an AFO with varying stiffness. Predictions were based on the objective of minimizing mCoT, loading rates at impact and head accelerations at each stiffness level, and the motor patterns were determined via dynamic optimization. The predictive gait simulation results were compared to experimental data from subjects with bilateral plantar flexor weakness walking with varying AFO stiffness. Our simulations demonstrated that reductions in mCoT with increasing stiffness were attributed to reductions in quadriceps metabolic cost during midstance. Increases in mCoT above optimum stiffness were attributed to the increasing metabolic cost of both hip flexor and hamstrings muscles. The insights gained from our predictive gait simulations could inform clinicians on the prescription of personalized AFOs. With further model individualization, simulations based on mCoT minimization may sufficiently predict adaptations to an AFO in individuals with plantar flexor weakness.

1 Abstract 26 Neuromuscular disorders often lead to ankle plantar flexor muscle weakness, which impairs ankle 27 push-off power and forward propulsion during gait. To improve walking speed and reduce 28 metabolic cost of transport (mCoT), patients with plantar flexor weakness are provided dorsal-leaf 29 spring ankle-foot orthoses (AFOs). The mCoT during gait depends on the AFO stiffness where an 30 optimal AFO stiffness exists that minimizes mCoT. The biomechanics of why and how there exists a 31 unique optimal stiffness for individuals with plantar flexor weakness are not well understood. To 32 help understand why, we hypothesized that gait adaptations can be predicted by mCoT 33 minimization. To explain how, we hypothesized that the AFO would reduce the required support 34 moment and, hence, metabolic costs from the ankle plantar flexor and knee extensor muscles during 35 stance and reduce hip flexor metabolic cost to initiate swing. 36 To test these hypotheses, we generated neuromusculoskeletal simulations to represent gait of an 37 individual with bilateral plantar flexor weakness wearing an AFO with varying stiffness. Predictions 38 were predicated on the goal of minimizing mCoT at each stiffness level, and the motor patterns were 39 determined via dynamic optimization. The simulation results were compared to experimental data 40 from subjects with bilateral plantar flexor weakness walking with varying  Our simulations demonstrated that minimization of mCoT predicts gait adaptations in response to 42 varying AFO stiffness levels in individuals with bilateral plantar flexor weakness. Initial reductions 43 in mCoT with increasing stiffness were attributed to reductions in quadriceps metabolic cost during 44 midstance. Increases in mCoT above optimum stiffness were attributed to the increasing metabolic 45 cost of both hip flexor and hamstrings muscles. 46 The insights gained from our simulations could inform clinicians on the prescription of personalized 47

Introduction 66
The plantar flexor muscles, consisting of soleus and the gastrocnemius, are often weakened in persons 67 with neuromuscular disorders, such as Charcot-Marie-Tooth disease and poliomyelitis [1] [2]. 68 Weakness of the plantar flexors results in an altered gait pattern, characterized by reduced push-off 69 power, and excessive ankle dorsiflexion and knee flexion during stance [3] [4]. These gait deviations 70 lead to a lower walking speed [5] and an elevated metabolic cost of transport (mCoT) [6], which limits 71 daily physical mobility [7]. Dorsal leaf spring (DLS) ankle-foot orthoses (AFOs) are often prescribed 72 to provide mechanical support during stance, augment push-off, and hence to reduce mCoT. In a 73 DLS-AFO, a leaf spring connects a footplate to a calf casing posterior of the ankle and passively 74 restricts ankle dorsiflexion by producing an external plantarflexion moment when the ankle is 75 dorsiflexed. As a spring, the AFO can store energy when moving into dorsiflexion and release this 76 energy as the ankle moves towards plantarflexion, thereby providing additional positive work 77 during push-off [8]. 78 In individuals with plantar flexor weakness, the effects of an AFO on improving gait kinematics and 79 kinetics and reducing mCoT have been shown to depend on the stiffness of the leaf spring [9][10] [11]. 80 Beginning at low and with increasing AFO stiffnesses, the mCoT first decreases, before increasing at 81 higher stiffness levels, demonstrating a convex relation between AFO stiffness and mCoT with an 82 optimum stiffness where mCoT is minimal [9] [10]. As demonstrated in healthy individuals 83 [12][13] [14], minimizing mCoT is prioritized during gait. As such, it can be expected that patients 84 with gait disorders prefer walking with the stiffness that minimizes their metabolic energy cost. In 85 case of plantar flexor weakness, the initial reduction in mCoT is thought to be the result of 86 normalizing ankle and knee angles and moments which requires adequate AFO stiffness [9] [10]. 87 Normalization of the ankle and knee biomechanics is hypothesized to lead to a decrease in the 88 metabolic cost of the quadriceps muscles and thereby reduce mCoT [15]. The initial decrease in mCoT 89 may be further explained by a reduction in the metabolic cost of the plantar flexors as the AFO 90 replaces the biological ankle plantarflexion moment during stance [11][16] [17]. However, at higher 91 . CC-BY 4.0 International license perpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The reduced ankle push-off work may result in higher energy losses at contralateral heel-strike and 94 lead to compensatory hip flexion work to initiate the swing phase [16], which are potential causes for 95 the increased mCoT at higher AFO stiffness levels. However, how each of these factors contribute to 96 the relation between AFO stiffness and mCoT in people with plantar flexor weakness is unknown. 97 The aim of this study was to gain insights into why and how mCoT is affected by AFO stiffness 98 variation in individuals with plantar flexor weakness by using predictive musculoskeletal 99 simulations. First, based on the assumption that mCoT is a predictor for gait pattern changes in 100 healthy individuals [14][12], we hypothesized that minimization of mCoT is a predictor of kinematic, 101 kinetic, and mCoT changes to varying AFO stiffness in individuals with bilateral plantar flexor 102 weakness. Second, we tested whether initial reductions in mCoT with increasing stiffness are 103 explained by i) decreasing metabolic cost of the quadriceps as the knee moments are normalized, and 104 ii) decreasing metabolic cost of the plantar flexors as the AFO replaces the ankle plantar-flexion 105 moment during stance phase. Third, we hypothesized that increases in mCoT as stiffnesses exceed 106 the optimum stiffness are caused by the increasing metabolic cost of hip flexor muscles to initiate the 107 swing phase as total push-off power decreases. 108 109 . CC-BY 4.0 International license perpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in

Musculoskeletal model
117 Based on the model of Delp et al. [25][24], we created a model with 9 degrees of freedom (3 around 118 the pelvis and 1 around the hip, knee and ankle of each leg), actuated by 9 Hill-type muscles per leg 119 (tibialis anterior, soleus, gastrocnemius, vasti, rectus femoris, biceps femoris short head, biarticular 120 hamstrings, iliopsoas, gluteus maximus) in OpenSim 3.3 [21] [22]. We set the maximum isometric 121 muscle strength of the soleus and gastrocnemius muscles of both legs to 40% of normal healthy values 122 (i.e. 60% muscle weakness), to induce bilateral plantar flexor weakness. Additionally, we restricted 123 the ability to activate the plantar flexor muscles to 50%, to take into account that the weakened 124 muscles would completely fatigue if they would be maximally activated for 10-20% of the gait cycle 125 [26][27] [28]. We modified passive muscle and tendon parameters in the model to maintain similar 126 passive muscle forces as in the healthy model [20] [29]. We set the slow twitch fiber ratios according 127 to Johnson et al.[30] and Garrett et al.[31], similarly to Ong et al.[24]. We scaled the model according 128 to experimental marker data of one subject with bilateral plantar flexor weakness close to the group's 129 mean height (177 cm) and body mass (81 kg) from the experimental study [10]. 130 To model the forces between the ground and the foot, we used a compliant Hunt-Crossley contact 131 model [32]. We placed one contact sphere at the heel and one at the toe of each foot (Fig 1). We set the 132 force parameters (stiffness, dissipation and friction) according to Veerkamp et al.[33], and modelled 133 . CC-BY 4.0 International license perpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for this this version posted October 18, 2022. ; https://doi.org/10.1101/2022.10.14.512205 doi: bioRxiv preprint 6 the knee ligaments using a rotational spring (2 Nm/deg) and damper (0.2 Nm/deg/s) around the knee 134 joint if the knee angles were outside the 5-120 deg flexion range [20]. 135 We modelled each AFO as two rigid parts, including a calf casing and a footplate with their 136 experimental mass (calf casing: 0.2 kg, footplate and shoe: 0.5 kg) [10]. We attached the AFO parts 137 rigidly to the tibia and calcaneus, respectively (Fig 1). We modelled the stiffness of the AFO as two 138 linear torsional springs for ankle dorsiflexion and for plantarflexion. In order to match experimental 139 movement of the ankle within the AFO, the AFO did not deliver a moment in the neutral angle range, 140 i.e. between 4.5 deg plantarflexion and 2 deg dorsiflexion. In DLS-AFOs, this small range depends on 141 the material and manufactured geometry of the AFO, and its fit on the subject's leg. The neutral angle 142 range was defined from the ankle angle range during swing phase of the subject because in swing 143 phase the AFO exerts only small moments on the ankle joint [34].   The objective function (J) was comprised of desired high-level tasks during gait, where minimization 154 of mCoT ( mCoT) was the primary measure. The following measures were included in the objective 155 function to be minimized: 156 mCoT was the mCoT measure, which aggregated the total muscle metabolic cost divided by the 157 distance travelled. We computed the metabolic cost of each individual muscle, according to the 158 muscle metabolic model by Uchida et al. [38]. 159 . CC-BY 4.0 International license perpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for this this version posted October 18, 2022. ; https://doi.org/10.1101/2022.10.14.512205 doi: bioRxiv preprint PGait was a penalty on the deviations of the simulation from gait at a specified minimum velocity of 160 1.22 m/s, to match experimental data without falling down [10]. 161 We added PDOFLimAnkle and PDOFLimKnee penalties to keep the ankle angle and passive knee forces within 162 physiological limits. We gave penalties, when the ankle angle was outside of the [−60, 60] deg range 163 and when the absolute coordinate limit moment acting on the knee joint was larger than 5 Nm [20]. 164 PFGImpact was a penalty composed of the sum of the absolute ground reaction force derivative over the 165 simulation divided by the distance travelled, which was included to penalize high loading rates at 166 impact. 167 PHeadStab was a penalty for excessive head accelerations calculated as the sum of the absolute head 168 accelerations normalized by distance travelled [39] [40]. 169 The weights associated to these high-level tasks were wmCoT=1.5, wGait=10 9 , wDOFLimAnkle=0.1, 170 wDOFLimKnee=0.01, wFGImpact=0.05, wHeadStab=0.1. We chose the weights based on a previous study [20], but 171 adapted with a higher emphasis on JmCoT to test the hypothesis that energy cost minimization can 172 predict gait changes with AFO stiffness. 173 We ran the simulations for stiffness levels between 0 and 7 Nm/degree, with steps of 1 Nm/degree. 174 We ran 5 optimizations in parallel with different random seeds in each round. Each optimization was 175 terminated when the average reduction of the cost function score in the last 200 generations was 176 smaller than 0.01 %. As initial guess, we used a controller with parameters resulting in healthy gait 177 [20]. We set the initial step size ( ), as the initial standard deviation of the parameters, to 0.05 [41]. 178 To check the robustness of our results, we ran multiple optimizations in sequence. We used the best 179 results of an optimization to initialize the next optimization with the same model (same AFO stiffness 180 setting) and the same initial step size, similar to Song et al. [37] and Ong et al. [41]. Since the trend of 181 the results was not changing qualitatively between the first and second round of optimizations, we 182 performed only two rounds of optimizations. We considered the results of the second round as the 183 final results. 184 . CC-BY 4.0 International license perpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in To test whether mCoT is a good predictor of the gait changes with varying AFO stiffness, we 186 compared our predictive simulations with experimental gait and mCoT data of 24 bilateral weakness 187 subjects walking with 5 different AFO stiffness configurations (2.8, 3.5, 4.3, 5.3, 6.6 Nm/deg) [10]. In 188 this experimental study, the mean mCoT (in J/kg/m) was evaluated from a 6-min comfortable walk 189 test with simultaneous gas-analysis over the last three minutes of the test. The study assessed gait 190 kinematics, kinetics and ground reaction forces with a 3D gait analysis on a 10-meter walkway using 191 the PlugInGait marker model [42]. Based on these measurements, clinically important gait features 192 for the evaluation of AFOs, e.g. the peak ankle dorsiflexion angle, ankle power, knee angle, knee 193 moment and AFO-generated power, were calculated using a custom-made script in MATLAB ® 194

R2015b (MathWorks Inc.). 195
To calculate the joint moments from the predictive simulations, we processed the simulation results 196 with the Analysis Tool in OpenSim. Based on the joint angles and moments, we calculated the joint 197 powers (Fig 2). To calculate negative and positive joint work over the whole gait cycle and separate 198 gait phases we used trapezoidal numerical integration of the joint power. We divided the gait cycle 199 into gait phases according to the definitions of Whittle [43]. These gait phases were: loading response, 200 midstance, push-off comprising of terminal stance and preswing, and swing. In order to assess the 201 source of the mCoT in detail, we calculated the simulated muscle metabolic energy cost [38] over 202 whole gait cycles, and different gait phases, for all 9 muscles. We normalized the metabolic cost by 203 body mass, mean walking speed and simulation duration to get the total metabolic cost over a gait 204 cycle in J/kg/m. We used a custom-made script in MATLAB ® R2020b (MathWorks Inc.) for all 205

calculations. 206
To compare simulation-based outcome measures to experimental observations, we calculated the 207 effect of 1 additional Nm/degree in stiffness for both the simulations and experimental data using a 208 linear fit across the stiffness levels for the following key gait features: peak ankle dorsiflexion angles, 209 peak total-, biological-and AFO ankle joint moments and powers, peak knee extension angles and 210 . CC-BY 4.0 International license perpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for this this version posted October 18, 2022. ; https://doi.org/10.1101/2022.10.14.512205 doi: bioRxiv preprint 9 peak knee joint moments (between 35-50% of gait cycle) [10]. We assessed the goodness of fit of the 211 curve by its coefficient of determination value (Rsq), calculated in MATLAB ® R2020b (MathWorks 212 Inc.) [44]. To assess the similarity between the simulated and experimentally obtained slopes, we 213 expressed the difference in slope in standard deviation of the experimental slope based on the 24 214 patients. 215 216 . CC-BY 4.0 International license perpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for this this version posted October 18, 2022. ; https://doi.org/10.1101/2022.10.14.512205 doi: bioRxiv preprint

217
Our predictive gait simulations took 20.46 hours on average to complete on an AMD Ryzen 9 3950X 218 (16 CPUs -32 virtual cores with hyperthreading, 3.5 GHz base) computer on 10 parallel threads. The 219 primary objective of mCoT minimization contributed to about 90% of the final optimization scores in 220 all simulations. In the final simulations, PGait and PDoFLimAnkle were optimized to zero and did not 221 contribute to the objective score. An overview of the simulated joint angles, moments and powers for 222 varying AFO stiffness levels are presented in Fig 2.

229
The predicted slopes of peak total, biological and AFO-provided ankle joint moment and power, 230 peak ankle dorsiflexion angle, peak knee extension angle and peak internal knee flexion moment 231 were all within 1.2 standard deviations (SD) of the experimental data. The highest slope difference 232 was found for peak total ankle moment and peak AFO moment, where a larger effect of additional 233 stiffness was predicted by the simulations than found in experimental data. Peak total ankle 234 moment was approximately constant in the experiments but showed an increasing trend in the 235 simulations (Fig 2, Fig 3 and S1 Table). 236

240
. CC-BY 4.0 International license perpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for this this version posted October 18, 2022. ; https://doi.org/10.1101/2022.10.14.512205 doi: bioRxiv preprint Simulated AFO effects on mCoT and muscle metabolic 241 consumption 242 The mCoT showed a clear minimum with increasing stiffness in both the simulated and individual 243 experimental results (Fig 4). The simulations presented a strong quadratic trend, Rsq = 0.836, while 244 the average experimental results showed a less pronounced quadratic trend, Rsq = 0.634, due to large 245 inter-subject variability (Fig 4). 246

256
The largest change in metabolic cost of individual muscles was found in the vasti, which also showed 257 a quadratic trend (Rsq = 0.928). In contrast, the metabolic cost of the hamstrings and iliopsoas 258 increased continuously. Both the soleus and gastrocnemius metabolic cost did not change 259 substantially with increasing AFO stiffness (Fig 5 and S2 Table). Gluteus maximus, tibialis anterior, 260 rectus femoris and biceps femoris short head muscles did not show any change with increasing AFO 261 stiffness (S2 Table). 262

266
. CC-BY 4.0 International license perpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for this this version posted October 18, 2022. ;https://doi.org/10.1101https://doi.org/10. /2022 Joint work and muscle metabolic consumption per gait phase 267 Total knee joint work did not differ with increasing AFO stiffness during the loading response, while 268 vasti metabolic cost decreased and hamstrings metabolic cost increased, especially above 3 269 Nm/degree. In midstance, positive knee joint work decreased, negative knee joint work increased and 270 vasti metabolic cost decreased, while hamstrings metabolic cost did not show a clear trend with 271 increasing AFO stiffness. (Fig 6, S3 and S4 Table). 272 During loading response, negative biological ankle work decreased with increasing AFO stiffness, 276 while no effect of stiffness on AFO work was found. Similarly, no effect on the metabolic cost of the 277 soleus or gastrocnemius was found with increasing stiffness. In midstance, negative biological ankle 278 joint work decreased and negative AFO work increased with increasing stiffness. Soleus metabolic 279 cost increased slightly until 5 Nm/deg AFO stiffness. During push-off, biological ankle work, AFO 280 work, and soleus metabolic cost increased until 3 Nm/deg. At higher stiffnesses, biological ankle work 281 generation and soleus metabolic cost decreased again (Fig 7, S3 and S4 Table). 282

286
During loading response, negative hip joint work decreased and hamstrings metabolic cost 287 increased with increasing stiffness. In early midstance, positive hip joint work increased, and in late 288 midstance, negative hip joint work and iliopsoas metabolic cost increased with increasing AFO 289 stiffness (Fig 8, S3 and S4 Table).

293
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294
The aim of this study was to gain insights into why and how motor pattern adaptations in people 295 with bilateral plantar flexor weakness result in an optimal AFO stiffness to minimize mCoT. As 296 hypothesized, our results showed that minimization of mCoT predicts most of the kinematic, kinetic, 297 and mCoT changes due to varying AFO stiffness in this population. Initial reductions in mCoT with 298 increasing stiffness were attributed to reductions in quadriceps metabolic cost, as hypothesized, but 299 in contrast to our hypothesis, plantar flexor metabolic cost did not decrease. Increases in mCoT above 300 the optimum AFO stiffness were attributed to the increasing metabolic cost of both hip flexor muscles 301 and hamstrings muscles. 302 The mCoT appears to be a good predictor of gait changes in individuals with bilateral plantar flexor 303 weakness wearing AFOs with varying stiffness. Our forward simulations predicted changes in lower 304 extremity kinematics and kinetics due to AFO stiffness variations within 1.2 SD of the experimentally 305 observed changes. Although mCoT was not the only factor within our objective function, it had by 306 far the largest contribution as it was responsible for 90% of the final objective function values. These 307 findings support the claims that humans tend to minimize mCoT when walking as previously 308 demonstrated in healthy subjects [12][13] [14] and in simulations of patients walking without assistive 309 devices [45]. 310 Differences between simulated and experimental data were found in the knee joint angle and moment 311 curves (Fig 2). Although the effects of varying AFO stiffness on specific gait features at midstance 312 were predicted reasonably well, in early stance the knee angle and moment became more extended 313 with increasing AFO stiffness (Fig 2 and 3 knee. Although loading rates were penalized in our simulations, loading rates still increased up to 318 . CC-BY 4.0 International license perpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for this this version posted October 18, 2022. ;https://doi.org/10.1101https://doi.org/10. /2022 14 twice as much as found in healthy subjects as AFO stiffness increased (S1 Fig),  The convex mCoT trend with respect to AFO stiffness can be explained by the metabolic cost changes 321 in the quadriceps (vasti), hip flexor (iliopsoas) and hamstrings muscles. This parabolic trend was also 322 present in the individual experimental data [10] (Fig 4). As hypothesized, initial reductions in mCoT 323 starting at low and with increasing AFO stiffness were due to a decrease in the metabolic cost of the 324 quadriceps (vasti) muscles (Fig 5). From low to medium AFO stiffnesses, the knee angle and moment 325 normalized, reducing the metabolic cost of the vasti [46] [48]. At higher stiffness levels, the knee 326 became increasingly extended, which minimized mCoT but might cause knee pain in real life [51] [52]. 327 Contradicting our hypothesis and experimental data in healthy subjects [53], metabolic cost of the 328 plantar flexor muscles did not decrease with increasing AFO stiffness. As muscle activation and 329 metabolic cost changes are related factors, our simulation result was also contrary to the findings of 330 Harper et al. [18] who found reductions in medial gastrocnemius muscle activation with increasing 331 AFO stiffness in lower limb salvage patients [18]. We likely did not observe reductions in plantar 332 flexor metabolic cost, because the low muscle strength in the model resulted in proportionally low 333 muscle mass, which reduces the muscle's contribution to metabolic cost [29], and hence, even without 334 an AFO the plantar flexors did not contribute substantially to mCoT. 335 In agreement with our hypothesis, increases in mCoT above the optimum stiffness were partly due 336 to increases in the metabolic cost of the hip flexor (iliopsoas) muscles. Iliopsoas metabolic cost 337 increased at the end of midstance before the start of push-off, potentially as a pre-activation to help 338 initiate the swing phase. Increased hip work was also shown in an experimental study in patients 339 with chronic stroke or multiple sclerosis where 0.5-5.4 Nm/deg AFO stiffnesses were tested [16]. 340 Additionally, an increase in metabolic cost of the hamstrings muscles added to the increase in mCoT 341 above the optimum stiffness. This metabolic cost increase can be seen during early stance where 342 slightly more extended hip joint angles, larger hip extension moments (Fig 2) and decreasing negative 343 hip joint work (Fig 8) can also be observed as AFO stiffness increases. At high stiffness levels, the hip 344 . CC-BY 4.0 International license perpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for this this version posted October 18, 2022. ; https://doi.org/10.1101/2022.10.14.512205 doi: bioRxiv preprint 15 is more extended at initial contact, and hip flexion is reduced during loading response that further 345 contributes to the increased knee joint loading rates at high stiffness. 346

Limitations and future work 347
To test our hypotheses, we used a simplified, planar musculoskeletal model where medio-lateral 348 stabilization was excluded, which could explain why our mCoT results were ∼10% lower [54] than 349 in the experiments. With suboptimal AFO settings, the out-of-plane compensation, such as trunk 350 motions, are known to be more extreme [55], hence the sensitivity of the mCoT trend to AFO stiffness 351 could be higher in reality than in our simulations. 352 In the experimental study that was used for comparison, only AFOs with a stiffness in the range of 353 2.8-6.6 Nm/deg were tested. Hence, we were unable to verify the validity of our prediction with low 354 stiffness levels. 355 In the future, simulations might be used to predict the individual optimal AFO properties, for which 356 improving our understanding of the underlying mechanisms in this study was an essential first step. 357 To be able to accurately predict adaptations to an AFO at the level of an individual, out-of-plane 358 degrees of freedom and muscle actions should be investigated to understand the affects out-of-plane 359 compensations. Furthermore, sensitivity analyses should be performed to evaluate the effect of 360 patient and device characteristics, such as body weight, muscle weakness and muscle spasticity, and 361 the neutral angle range of the AFO, have on the optimal AFO stiffness. With individualized models, 362 our forward simulations could help predict the individual adaptations of patients to an AFO and 363 improve the prescription of AFO settings. 364

Conclusion 365
We showed that adaptations in gait mechanics due to varying AFO stiffness, in individuals with 366 bilateral plantar flexor weakness, can be predicted by minimization of mCoT. Our simulation results 367 demonstrate the convex relation between mCoT and AFO stiffness, and are able to explain this shape 368 by decreases in quadriceps metabolic cost in midstance, and increases in metabolic cost of the 369 . CC-BY 4.0 International license perpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in

453
. CC-BY 4.0 International license perpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for this this version posted October 18, 2022. ; https://doi.org/10.1101/2022.10.14.512205 doi: bioRxiv preprint